

Class . 
Book_ 


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THE 



CARPENTER'S AND JOINER'S 

HAND-BOOK: 



CONTAINING 

A COMPLETE TREATISE ON FRAMIXG 
HIP AND VALLEY ROOFS. 

TOGETHER WITH 

MUCH VALUABLE INSTRUCTION FOR ALL MECHANICS AND 

AMATEURS, USEFUL RULES, TABLES, ETC., 

NEVER BEFORE PUBLISHED 



/ . BY 

rr 
PEACTICAL AKCniTECT AND BFILDEK, 



ILLUSTRATED BY THIRTY-SEYEN ENGRAVlNaS. 



NEW YORK : 

JOHN WILEY & SOX, 535 BROADWAY, 

1867. 






Entered according to Act of Congress, in the year 1868, 

By H. W. holly, 

In the Clerk^s Office of the District Court of the United States for 
the District of Connecticut 

By Transfer from 
U.S. Naval Academy 
Aug. 26 1932 



# 



sit 



4 

^ PEEFACE, 



This work has been undertaken by the 
antbor to supply a want long felt by tbe 
trade: tbat is, a cbeap and convenient 
"Pocket Guide/' containing tbe most use- 
ful and necessary rules for tbe carpenter. 

Tbe writer, in bis progress " tbrougb tbe 
mill," bas often felt tbat sucb a work as tbis 
would bave been of great value, and some 
one principle bere demonstrated been worth 
many times tbe cost of tbe book. 

It is believed, tberefore, tbat tbis book will 
commend itself to tbose interested, for tbe 
reason tbat it is cbeap, tbat it is plain and 
easily understood, and tbat it is useftd. 



CONTENTS. 



AET. 

To find the lengths and bevels of hip and common 

rafters 1 

To find the lengths, &c., of the jacks 2 

To find the backing of the hip , 3 

Position of the hip-rafter 4 

Where to take the length of rafters 5 

Difierence between the hip and valley roof 6 

Hip and vaUey combined *l 

Hip-roof without a deck 8 

To frame a concave hip-roof 9 

An easy way to find the length, &c., of common 

rafters 10 

Scale to draw roof plans 11 

To find the form of an angle bracket 12 

To find the form of the base or covering to a cone. . . 13 

To find the shape of horizontal covering for domes. . 14 

To divide a line into any number of equal parts 15 

To find the mitre joint of any angle 16 

To square a board with compasses 17 

To make a perfect square with compasses 18 

To find the centre of a circle 19 

To find the same by another method 20 

Through any three points not in a line, to draw a 

circle 21 

Two circles being given, to find a third whose area 

shall equal the first and second 22 



6 CONTENTS. 

▲ST. 

To find the form of a raking crown moulding 23 

To lay out an octagon from a square 24 

To draw a hexagon from a circle 25 

To describe a curve by a set triangle 26 

To describe a curve by intersections 2*1 

To describe an elliptical curve by intersection of 

lines 28 

To describe the parabolic curve 29 

To find the joints for splayed work 30 

Stairs 31 

To make the pitch-board 32 

To lay out the string 33 

To file the fleam-tooth saw 34 

To dovetail two pieces of wood on four sides 35 

To splice a stick without shortening 36 

The difference between large and small files 3*7 

Piling wood on a side-hill 38 

To find the number of gallons in a tank 39 

To find the area of a circle 40 

Capacity of wells and cisterns 41 

"Weights of various materials 42 



THE CARPENTER'S AND JOINER'S 

HAND-BOOK- 



HIP AND VALLEY EOOFS. 

The framing of liip and valley roofs, being 
of a different nature from common square 
rule framing, seems to be^ understood by 
very few. It need scarcely be said, that it is 
very desirable that this important part of a 
carpenter's work should be familiar to 
every one who expects to be rated as a first- 
class workman. The system here shown is 
proved, by an experience of several years, 
to be perfectly correct and practicable ; and, 
as it is simple and easily understood, it is 
believed to be the best in use. Care has 
been taken to extend the plates so as to de- 



8 



THE carpenter's 



monstrate eacli position or principle by it- 
self, so that the inconvenience and confusion 
of many lines and letters mixed np with 
each other may be avoided. 

Article 1. — To find the lengths and levels 
of hip and common rafters. 




Fig. 1. 



Let j9jf>jp (Fig. 1) represent the face of the 
plates of the building ; d^ the deck-frame : 



hand-book:. 9 

a is tlie seat of the hip-rafter; 5, of the 
jack ; and c^ of the common rafter. Set the 
rise of the roof from the ends of the hip and 
common rafter towards e e^ square from a 
and G / connect^ and e^ then the line from 
fioe will be the length of the hip and com- 
mon rafter, and the angles at ^ ^ will be the 
down bevels of the same. 

2. To find the length andhevel of the jack- 
rafters, 

l (Fig. 1) is the seat of a jack-rafter. Set 
the length of the hip from the corner, g^ to 
the line on the face of the deck-frame, and 
join it to the point at g. Extend the jack h 
to meet this line at A/ then from i to A will 
be the length of the jack-rafter, and the 
angle at h will be the top bevel of the same. 

The length of all the jacks is lound in the 
same way, by extending them to meet the 
line A. The dov^n bevel of the jacks is the 
same as that of the common rafter at e, 

3. To find the hacking of the hip-rafter. 
At any point on the seat of the hip, a (Fig. 



10 THE CAEPENTER's 

1), draw a line at riglit angles to a^ extending 
to the face of the plates at ^ ^ / upon the 
points where the lines cross, draw the half 
circle, just touching the line/*^; connect the 
point aty, where the half circle cuts the line 
a^ with the points ^ ^ / the angle formed at^ 
will be the proper backing of the hip-rafter. 

It is not worth while to back the hip-raf- 
ter unless the roof is one-quarter pitch or 
more. 

4. It is always desirable to have the hip- 
rafters on a mitre line, so that the roof will 
all be the same pitch ; but when for some 
reason this cannot be done, the same rule is 
employed, but the jacks on each side of the 
hip are different lengths and bevels. 



HAND-BOOK, 



11 




Fig. 2. 

The heavy line from d (Fig. 2), shows the 
seat of the hip-rafter ; a and 5, the jacks. Set 
the rise of the roof at e / set the length of 
the hip d e^ from d to/* on one side of the 
deck, and from dio g on the other side ; ex- 
tend the jack 5, and all the jacks on that 
side, to the line df^ for the length and top 
bevels ; extend the jack a^ and all on that 
side, to the line d g^ for the length and bevels 
on that side of the hip. The down bevels 
of the jacks will be the same as that of the 
common rafters on the same side of the 
roof. 



12 



THE CAEPENTER S 



5. The lengths of hips, jacks, and valley- 
rafters should be taken on the centre line, and 
the thickness or half thickness allowed for. 
(See Fig. 3.) 




Fig. 3. 

6. The valley-roof is the same as the hip- 
roof inverted. The principle of construction 
is the same, with a little different applica- 
tion. 



HAKD-BOCK. 



13 




Fig. 4. 



Let a h (Fig. 4) represent the valley-rafter ; 
j j are corresponding jack-rafters. Set the 
rise of the roof from aio c ; connect h and 
c : from J to ^ is the length of the valley- 
rafter, and the angle at c the bevel of the 
same ; set the length h c on the line from a; 
extend the jack^ to meet the line o d at e f 
then from etof is the length of the jack, 
and the angle at e the top bevel of the same. 

7. When the hip and valley are combined^ 



14 



THE carpenter's 



SO that one end of tliejack is on the hip^ and 
the other 07i the valley. 




Fig. 5. 

a h (Fig. 5) is the liip, and c d the valley- 
rafters. Find the length of each according 
to the previous directions ; find the lines e 
and/* as before. 

Extend the jacks j j to the line e^ for the 
top bevel on the hip : extend the same on 
the other end to the line/*, for the top bevel 
on the valley ; the whole lengths of the jacks 



>*!> 



HAND-BOOK. 



15 



is from the line/* to the line e. If the hip 
and valley rafters lie parallel, the bevel will 
be the same on each end of the jack. 

8. In framing a hip-roof without a deck- 
ing or observatory, a ridge-pole is nsed, and 
of such a length as to bring the hip on a 
mitre line; but this ridge-pole must be cut 
half its thickness longer at each end, or the 
hip will be thrown out of place and the 
whole job be disarranged. 




Fisr. 6. 



This is illustrated by the figure. Suppose 
the building to be 16 by 20, the ridge would 
require to be four feet long ; but if the stick 
is four inches thick, for instance, then it 



16 



THE CARPENTER S 



should be cut four feet four inclies long, so 
that the centre line on the hip, a, will point 
to the centre of the end of the ridge-pole, 
J, at four feet long. This simple fact is often 
overlooked. 

9. To frame a concave hip-roof. — (This 
is much used for verandas, balconies, sum- 
mer-houses, &c.) 




To find the curve of the hip. 
Let a (Fig. 7) be the common rafter in its 
true position, the line h being level. Draw the 



HAND-BOOK. 17 

line G Cj on the angle the hip-rafter is to lie, 
generally a mitre line ; draw the small lines 
0^ parallel to the plate j9. The more of these 
lines, the easier to trace the curve ; continue 
the lines o o o^ where they strike the line c c^ 
square from that line ; set the distances 1, 2, 
3, 4, &c. (on a^ from the line V) on the line 
G G^ towards e^ at right angles from c g ; 
through these points, 2, 4, 6, 8, &c., trace 
the curve, which will give the form of the 
hip-rafter. 

To get the joints of the jack-rafters, take 
a piece of plank d^ (Fig. 7), the thickness 
required, wide enough to cut a common 
rafter; mark out the common rafter the 
full size. Then get the lengths and bevels, 
the same as a straight raftered roof, which 
this will be, looking down upon it from 
above; then lay out your joints from the 
top edge of the plank, as/y ; cut these joints 
first, saw out the curves afterwards, and you 
will have your jacks all ready to put up. 
Cut one jack of each length by this method, 



18 THE carpenter's 

then use this for a pattern for the others, so 
as not to waste stuff. It will be seen that 
the down bevel is different on each jack, 
from the curve^ but the same Jfrom a straight 
line, from point to point of a whole rafter. 

10. A quick and easy way to find the 
lengths and hevels of common rafters. 

Suppose a building is 40 feet wide, and 
the roof is to rise seven feet. Place your 
steel square on a board (Fig. 8), twenty- 
inches from the corner one way, and seven 
inches the other. The angle at c will be 
the bevel of the upper end, and the angle 
at d^ the bevel of the lower end of the rafter. 




Fiff. 8. 



11. The length of the rafter will be from 
a to J, on the edge of tlie board. Always buy 
a square with the inches on one side divided 



HAKD-BOOK. 



19 



into twelfths, then you have a convenient 
scale always at hand for such work as this. 
The twenty inches shows the twenty feet, 
half the width of the building ; the seven 
inches, the seven foot rise. Now the distance 
from a to 5, on the edge of the board, is 
twenty-one inches, two-twelfths, and one- 
quarter of a twelfth, therefore this rafter will 
be 21 feet 2^ inches long. 

12. To find the form of an angle IracTcet 
for a cmmice. 




Fig. 9. 



Let a (Fig. 9) be the common bracket ; 
draw the parallel lines o o o, to meet the 



20 



THE CARPENTER S 



mitre line c ; square up on each line at c, 
and set the distances 1, 2, 3, 4, (fee, on the 
common bracket, jfrom the line d^ on the 
small lines from c ; through these points, 2, 
4, 6, &c., trace the form of the bracket. 
This is the same principle illustrated at Fig. 
7 and Fig. 20. 

13. To find the form of a lase or covering 
for a cone. 




Fiff. 10. 



Let a (Fig. 10) be the width of the base 
to the cone. Draw the line h through the 
centre of the cone ; extend the line of the 
side G till it meets the line h ^i d ; on d for 
a centre, with 1 and 2 for a radius, describe 



HAND-BOOK. 



21 



e^ wluch will be the shape of the base re- 
quired; y*will be the joint required for the 
same. 

14. To find the shape of horizontal cover- 
ing for circular domes. 

The principle is the same as that employed 
at Fig. IO5 supposing the surface of the dome 
to be composed of many plane surfaces. 
Therefore, the narrower the pieces are, the 
more accurately they will fit the dome. 



d 


fl 


yT 


9 ^ry 


/ 


-- fc ^ ^ 


/ 


s\ 


1 


4\ 


I ^ 


\ 


1 c 


i 



Fig. 11. 



Draw the line a through the centre of the 
dome (Fig. 11) ; divide the height from h to 



THE CAEPENTEr's 



c into as many parts as there are to be ' 
courses of boards, or tin. Throngli 1 and 2 
draw a line meeting tbe centre line at d ; 
that point will be the centre for sweeping 
the edges of the board g. Through 2 and 
3, draw the line meeting the centre line at 
e / that will be the centre for sweeping the 
edges of the board Tc^ and so on for the other 
courses. 

15. To divide a line into any number of 
equal parts. 




Let a h (Fig. 12) be the given line. Draw 
the line a c^ at any convenient angle, to ah ; 
set the dividers any distance, as from 1 to 2, 
and run off on a c^ as many points as you 
wish to divide the line a l into ; say 7 parts ; 



HAND-BOOK. 23 

connect tlie point -7 with l^ and draw the 

lines at 6, 5, 4, (fee, parallel to the line 7 

5, and the line a l will be divided as desired. 

16. To find the mitre joint of any angle. 




Fig. 13. 

Let a and h (Fig. 13) be the given angles ; 
set off from the points of the angles equals 
distances each way, and from those points 
sweep the parts of circles, as shown in the 
figure. Then a line from the point of the 
angle through where the circles cross each 
other, will be the mitre line. 



24 THE carpenter's 

17. To square a hoard with compasses. 




Fig. 14. 

Let a (Fig. 14) be the board, and h the 
point from which to square. Set the com- 
passes from the point h any distance less 
than the middle of the board, in the direc- 
tionof e. Upon c for a centre sweep the 
circle, as shown. Then draw a straight line 
from where the circle touches the lower edge 
of the board, through the centre c^ cutting 
the circle at d. Then a line from h through 
6?, will be perfectly square from the lower 
edge of the board. This is a very useful 
problem, and will be found valuable for lay- 
ing out walks and foundations, by using a 
line or long rod in place of compasses. 



hand-book:. 



25 



18. To make a perfect square with a. jpair 
of compasses. 




Tiff. 15. 



Let a I (Fig. 15) be tlie length of a 
Bide of the proposed square ; upon a and h^ 
with the whole length for the radius, sweep 
the parts of circles a d and h c. Find half 
the distance from a to e at f ; then upon e 
for a centre sweep the circle cutting/*. Draw 
the lines from ^ and 5, through where the 
circles intersect at c and d / connect them 
at the top and it will form a perfect square. 



26 THE carpenter's 

19. To find the centre of a circle. 




Upon two points nearly opposite each 
other, as (3^ & (Fig. 16), draw the two parts 
of circles, cutting each other ^X c d ; repeat 
the same at the points e f ; draw the two 
straight lines intersecting at ^, which will 
be the centre required. 



HAND-BOOK. 

20. Another method. 



27 




Fig. IT. 

Lay a square upon the circle (Fig. 17), 
with the corner jnst touching the outer edge 
of the circle. Draw the line a^l) across the 
circle where the outside edges of the square 
touch it. Then half the length of the line a 
h will be the centre required. No matter 
what is the position of the square, if the cor- 
ner touches the outside of the circle, the re- 
sult is the same, as shown by the dotted 
lines. 



28 THE carpenter's 

21. Through any three points not in a line^ 
to draw a circle. 




Fiff. 18. 



Let a h c (Fig 18) be the given points. 
Upon each of these points sweep the parts 
of circles, cutting each other, as shown in the 
figure ; draw the straight lines d d^ and where 
they intersect each other will be the centre 
required. This method may be employed 
to find the centre of a circle where but part 
of the circle is given, as from a to c, 

22. Two circles 'being given^ to find a third 
whose surface or area shall equal the first 
and second. 



HAND-BOOK, 



29 




Fig. 19. 

Let a and h (Fig. 19) be tlie given circles. 
Place the diameter of each at right angles to 
the other as at 3, connect the ends at c and 
dy then c d will be the diameter of the 
circle required. 

23. To find the form of a raking crown 
moulding. 




Fij?. 20. 



30 THE carpenter's 



m (Fig. 20) is the form of the level crown 
moulding; r c h the pitch of the roof. 
Draw the line l^ which shows the thickness 
of the moulding. Draw the lines o o o, par- ' 
allel to the rake. Where these lines strike 
the face of the level moulding, draw the hor- 
izontal lines I5 2, 3, &c. Draw the line y 
square from the rake : set the same distances 
from this line that you find on the level 
moulding 1, 2, 3, &c. Trace the curve 
through these points 1, 2, 3, cfec, and you 
have the form of the raking moulding. 

Hold the raking moulding in the mitre 
box, on the same pitch that it is on the roof, 
the box being level, and cut the mitre in 
that position. 

24. To make an octagon^ or eight-sided 
figure^ from a square. 



HAND-BOOK. 



31 




Fiff. 21. 



Let Fig. 21 be the square ; find tlie centre 
a J set tlie compasses from the corner J, to 
a ; describe the circle cutting the outside line 
at c and d ; repeat the same at each corner, 
and draw lines c e^ f g\lid^ and ij. These 
lines will form the octagon desired 

25. To draw a hexagon or six-sided fig- 
ure on a circle. 

Each side of a hexagon drawn within ar 
circle is just half the diameter of that circle. 
Therefore in describing the hexagon (Fig. 22), 
first sweep the circle ; then without altering 
the compasses, set off from a to &, from h to <?, 
and so on. Join all these points, a^ J, <?, 



32 



THE CARPENTER S 




&c., and you have an exact hexagon. Join 
V J, d^ and/*, and you have an equilateral tri- 
angle ; join d^ e^ and the centre, and you 
have another triangle, just one-sixth of the 
hexagon described. 

26. To describe a curve hy a set triangle. 




Fig. 23. 



Let a h (Fig. 23) be the length, and c d 
the height of the curve desired ; drive two 



HAND-BOOK. 33 

pins or awls at e and e / take two strips s Sy 
tack them together at d, bring the edges out 
to the pins at e/ tack on the brace /*, to 
keep them in place; hold a pencil at the 
point d; then move the point d^ towards e, 
both ways, keeping the strips hard against 
the pins at e^ e^ and the pencil will describe 
the curve, which is a portion of an exact cir- 
cle. If the strips are placed at right angles, 
the curve will be a half circle. 

This is a quick and convenient way to get 
the form of flat centres, for brick arches, 
window and door heads, &c. 




Fig. 24. 

27. Fig. 24 shows the method of forming 

a curve by intersection of lines. If the 

points 1, 2, 3, &c., are equal on both sides. 

the curve will be part of a circle. 
3* 



34 



THE CARPENTER S 



28. Fig. 25 sliows how to form an ellipti- 
cal curve by intersections. Divide the dis- 
tance a J, into as many points as from 5 to <?, 







-/ 


2. 


5 


4- 








J ^ 


^^-^ 


.-^^^ 


c 


^°~*^^^ 


\ 


-* 


J. 


^ 


.--^^ 






^^ 


^ 


e« 


5^ 












\ 


to 


/ 












\ 




Clf 








I 







Fig. 25. 

and proceed as in Fig. 24. The closer the 
points 1, 2, 3, &C.5 are together, the more 
accurate and clearly defined will be the 
curve, as at d, 

29. Fig. 26 shows the parabolio curve. 




Fig. 26. 



HAND-BOOK. 



35 



This is the form of the curve of the Gothic 
arch or groin. 

30. To find the joints for splayed work^ 
such as hojppers^ trays^ c&c. 




Fiff. 27. 



Take a separate piece of stuff to find the 
joints for the hopper, Fig. 27. Strike the 
bevel /^, the bevel of the hopper, on the 




Fig. 28. 



36 THE caiipent:e:k's 

end of the piece (Fig. 28) ; nm the gauge- 
mark G ivoTnf; then square on the edge from 
a^ or where you want the outside joint, to h; 
then square down from 5 to the gauge-mark 
G / strike the bevel of the work f g^ from i 
to d^ through the point at e. From a to d 
will be the joint, the inside corner the 
longest. If a mitre joint is wanted, set the 
thickness of the stuff, measuring onfg^ from 
d to h ; the line ^ A will be the mitre joint. 

31. Stairs,"^ — It is not practicable in a 
work of this size to go into all the details of 
stair-building, hand-railing, &c., but a few 
leading ideas on plain stairs may be intro- 
duced. 

First, measure the height of the story from 
the top of one floor to the top of the next ; 
also the run or distance horizontally from 
the landing to where the first riser is placed. 

* For a thorough treatise on stair-building in all its de- 
tails, and many other subjects of interest to the builder, 
I would recommend " The American House Carpenter," 
by IX. a. Hatfield, New York. 



• HAJS^D-BOOK. 37 

Suppose the height to be 10 ft. 4 in., or 124 
inches. As the rise to be easy should not 
be over 8 inches, divide 124 by 8 to get the 
number of risers : result, 15|^. As it does 
not come out even, we must make the num- 
ber of risers 16, and divide it into 124 inches 
for the width of the risers : result, 7f , the 
width of the risers. If there is plenty of 
room for the run, the steps should be made 
10 inches wide besides the nosing or projec- 
tion ; but suppose the run to be limited, on 
account of a door or something else, to 10 
ft. 5 in., or 125 inches : divide the distance 
in inches by the number of steps, w^hich is 
one less than the number of risers, because 
the upper floor forms a step for the last riser. 
Di^dde 125 by 15, which gives 8^ or 8/^ 
inches, the neat width x of the step, which 
with the nosing, will make about a 9J step. 
32. To make a pitch-hoard. { 

4 



38 



THE CARPENTERS 




^ 



Fiff. 29. 



Take a piece of tliin clear stuff (Fig. 29), 
and lay the square on the face edge, as 
shown in the figure, and mark out the pitch- 
board^ with a sharp knife. 

33. To lay out the string. 

Nail a piece across the longest edge of the 
pitch-board, as at Z>, so as to hold it up to 
the string more conveniently. Then begin 
at the bottom, sliding the pitch-board along 
the upper edge of the string, and marking it 
out, as shown at Fig. 30. 




Fig. 30. 



HAND-BOOK. 39 

The bottom riser mnst scribe down to the 
thickness of the step narrower than the 
others. 

34. To file the fleam-tooth saw. 

a 





Fig. 8t 

Fig. 31 shows the manner of filing the 
fleam, or lancet toothed saw. a shows the 
form of the teeth, full size ; and &, the position 
of holding the saw. The saw is held flat on 
the bench, and one side is finished before it 
y is turned over. No setting is needed, and 
the plate should be thin and of the very 
best quality and temper. 



40 



THE CARPENTER S 



These saws cut at an astonishing rate, cut- 
ting equally both ways, and cut as smooth 
as if the work were finished with the keenest 
plane. 

35. To dovetail two pieces of wood show- 
ing the dovetail on four sides. 







Fig. 32. 



a (Fig. 32) shows two blocks joined to- 
gether with a dovetail on fonr sides. This 



HAND-BOOK, 



41 



looks at first like an impossibility^ but h 
shows it to be a very simple matter. TMs 
is not of mncb practical nse except as a 
puzzle. I bave seen one of tbese at a fair 
attract great attention; nobody could tell 
how it was done. The two pieces should be 
of different colored wood and glued to- 
gether. 

36. To mend or splice a hroTcen stick with- 
out TRCtking it any shorter or itsing any new 
stuff. 

A vessel at sea had the misfortune to 
break a mast, and there was no timber of 
any kind to mend it. The carpenter ingeni- 
ously overcame the difficulty, without short- 
ening the mast. 



(V I c 



d 



1 


1 


/ 








A 








<l 




cl 


a 


t 


1 




\ 


_J 




; 







Jis:. 33. 



42 THE cakpenter's 

^ at 1 (Fig. 33) shows where the mast was 
broken. Cut the piece a 5, say three feet 
long, and the piece c d^ six feet long, half 
way through the stick. Take out these two 
pieces, keeping the two broken ends to- 
gether, turn them end for end, and put them 
back in place, as shown at 2. 

This arrangement not only brought the 
vessel safe home, but was considered by the 
owners good for another voyage. 

By putting hoops around each j.oint, the 
stick would be about as strong as ever. 

37. Is there any difference in the angle 
of a large or small three-cornered file ? 

Certainly not : for the file is an equilateral 
triangle, equal on all sides. 




Fig. 34 proves this, a is a file measuring 



HAND-BOOK. 



43 



one inch on all sides ; cut off hj making a 
file \ inch on the sides, it will readily be seen 
that the angle is exactly the same. 

Simple as this fact is, it is unknown to 
many. 

38. Does a pile of wood on a side hill 
piled perpendicularly^ eight feet long ^ four 
wide^ and four high^ contain a cord ? 

It does not. 



Fiff. 35. 



To illustrate, let us make a frame (Fig. 
35) just 4 by 8 in the clear. When this 
frame stands level it will hold just a cord. 



44 



THE CARPENTEKS 




Place tliis frame on a side hill, so as to give 
it the position in Fig. 36, it will be seen that 
the 8 ft. sides are brought nearer together, 
thus lessening its capacity. Continue to in- 
crease the steepness of the ground, as at Fig. 
37, or more, the 8 ft. sides would finally 




Fig. ST. 



HAND-BOOK. 45 

come together, and tlie frame contain noth- 
ing at all. It therefore becomes careful 
buyers of wood to consider where it is piled. 
39. To find the numher of gallons in a 
tanh or hox^ multiply the number of cubic 
feet in the tank by 7f . 

How many gallons in a tank 8 feet long, 
4 feet wide, and 3 feet high? 

8 

4 



32 
3 



96 cubic feet. 



672 

72 



Ans. 744 gallons. 



46 THE 


caepenter's 




40. To find the 


5 area or number of 


square 


feet in a circle. 






Three-quarters 


of tlie square of tlie diam- 


eter will give tlie 


area. 




What is the area of a circle Qft. in 


. diam- 


eter ? 


6 
6 

36 

f 




Ans, 


2T feet. 





For large circles, or where greater accu- 
racy is required, multiply the square of the 
diameter by the decimal .785. 



HAND-BOOK. 47 

41. Capacity of wells and cisterns. 
One foot in depth of a cistern : 

3 feet in diameter contains 65^ gallons, 
34 " " " 76 " 

4 " " " 98 " 
4i " " " 1241 " 

5 " " « 153i " 
5|- feet in diameter contains 186|^ " 

6 " " " 220i " 

7 " " " 300i " 

8 " " " 392i " 

9 " " " 497 " 
10 " " " 613i " 

A gallon is required by law to contain 
eight pounds of pure water. 



48 THE carpenter's 

42. Weights of various materials : 

Lbs. in a 
cubic foot. 

Cast-iron - - - - - 460 

Cast-lead - . - - - - 709 

Gold 1,210 

Platina 1,345 

Steel 488 

Pewter ----.. 453 

Brass - . ... 506 

Copper 549 

Granite 166 

Marble 170 

Blue stone - ... 160 

Pumice-stone - - - - 56 

Glass 160 

Chalk - - - - ' - - 150 

Brick 103 

Brickwork laid - - - - 95 

Clean sand - - - - 100 

Beech-wood - - * - - - 40 

Ash - - - - - - 45 

Birch - - - - - - 45 

Cedar - - - - - 28 



HAFD-BOOK. 49 

Lbs. in a 
cubic foot. 

Hickory 52 

Ebony .83 

Lignum-vitae - - - - 83 

Pine, yellow - - - - 38 

Cork 15 

Pine, white - - - - 25 

Birch charcoal - - - - 34 

Pine " - - . - 18 

Beeswax 60 

Water 62^ 

5 



